Is it mandatory to make up the missed prayers in order, such as if I missed the prayer (and) then the time for the Jama’ah of the next prayer comes in. So would I leave off the Jama’ah and make up the missed prayer?

It is a must to perform them in order. And it is possible to pray with the Jama’ah (by making your intention to make up) for the missed prayer, (and) then after it you can pray the current salaah except (meaning the only scenario in which you would not do this act is) in a state wherein you fear that the time for the current salaah will no longer be valid. For example, if the current salaah is salaatu ‘Asr, the ending of its time is by the sun becoming yellow (during its setting ). As for (if the purpose is merely to avoid) missing the congregation prayer, then it is still necessary to perform them in order

Reference: The Fataawa of Ash-Shaykh Abdul Azeez ar-Raajihi (excerpt from the app).